On the global well-posedness theory for a class of PDE models for criminal activity

Physica D: Nonlinear Phenomena

Volumn 260, Issue , 2013, Pages 191-200

  Rodriguez N ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Crime modeling; Global well posedness; Parabolic elliptic systems; Parabolic parabolic systems

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS; VELOCITY;

ADVECTION - DIFFUSION; CRIME MODELS; GLOBAL WELL-POSEDNESS; LOCAL WELL-POSEDNESS; PARABOLIC SYSTEM; PARABOLIC-ELLIPTIC SYSTEM; ROUTINE ACTIVITY THEORIES; SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS;

CRIME;

EID: 84885369979     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2012.08.003     Document Type: Article

References (26)

1. P. Biler, Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions, Nonlinear Anal. TMA 19 (12) (1992) 1121-1136.
2. P. Biler, T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction particles, I, Colloq. Math. 66 (1993).
3. P. Biler, D. Hilhorst, T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles, III, Colloq. Math. 68 (1995) 229-239.
4. P. Biler, W. Hebisch, T. Nadzieja, The Debye system: existence and large time behavior of solutions, Nonlinear Anal. 23 (9) (1994) 1189-1209.
5. P. Biler, Global solutions to some parabolic-elliptic systems of chemotaxis, Adv. Math. Sci. Appl. 9 (1) (1999) 347-359.
6. P. Biler, Local and global solvability of some parabolic systems modelling chemotaxis, Adv. Math. Sci. Appl. 8 (2) (1998) 715-743.
7. P. Biler, W. A. Woyczyñski, Global and exploding solutions for nonlocal quadratic evolution problems, SIAM J. Appl. Math. 59 (3) (1998) 845-869.
8. P. J. Brantingham, P. L. Brantingham, Crime Patterns, McMillan, 1987.
9. A. E. Bottoms, P. Wiles, Crime, Policing and Places: Essay in Environmental Criminology, Routledge, 1992, pp. 27-54.
10. L. E. Cohen, M. Felson, Social change and crime rate trends: a routine activity approach, Amer. Sociol. Rev. 44 (4) (1979) 588-608.
11. M. B. Short, M. R. D'Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi, L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci. 18(suppl.) (2008) 1249-1267.
12. J. Q. Wilson, G. L. Kelling, Broken windows and police and neighborhood safety, Atlantic Mon. 249 (1998) 29-38.
13. L. Anselin, J. Cohen, D. Cook, W. Gorr, G. Tita, Spatial analyses of crime, Criminal Justice 2000 4 (1998) 213-262.
14. S. Johnson, K. Bowers, The burglary as clue to the future: the beginnings of prospective hot-spotting, Eur. J. Criminol. 1 (2004) 237-255.
15. S. Johnson, K. Bowers, Domestic burglary repeats and space-time clusters: the dimensions of risk, Eur. J. Criminol. 2 (2005) 67-92.
16. S. Johnson, K. Bowers, A. Hirschfield, New insights into the spatial and temporal distribution of repeat victimization, Br. J. Criminol. 37 (1997) 224-244.
17. M. B. Short, M. R. D'Orsogna, P. J. Brantingham, G. E. Tita, Measuring and modeling repeat and near-repeat burglary effects, J. Quant. Criminol. 25 (3) (2009) 325-339.
18. N. Rodríguez, A. Bertozzi, Local existence and uniqueness of solutions to a PDE model for criminal behavior, Math. Models Methods Appl. Sci. 20 (2010).
19. R. Schaaf, Stationary solutions of chemotaxis systems, Trans. Amer. Math. Soc. 292 (2) (1985) 531-556.
20. 2, Commun. Math. Sci. 6 (2) (2008) 417-447.
21. 2, J. Differential Geom. 27 (2) (1988) 259-296.
22. Y. Benyamini, J. Lindenstrauss, Geometric Nonlinear Functional Analysis, in: Colloquium Publications, vol. 48, American Mathematical Society, Providence, RI, 2000.
23. R. E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, American Mathematical Society, Providence, RI, 1997.
24. O. A. Ladyženskaja, V. A. Solonnikov, N. N. Ural'ceva, Linear and Quasi-Linear Equations of Parabolic Type, Amer. Mathematical Society, 1968.
25. A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, Inc., New York, 1969.
26. T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, Amer. Mathematical Society, 2006.